The limit does not exist because the function is not defined at (x,y) = (0,0)You can see this by plugging in (x,y) = (0,0) into the function, you get 3(0^2) * 0 / (0^2 + 0^2) = 0 / 0 which is an indeterminate form.
Why is limit defined?In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Calculus and mathematical depend on limits, which are also used to determine integrals, derivative, and continuity.
What are types of limits?There are each limits (left- and proper limits), infinite limits, and limitations at infinity in addition to regular, two-sided limits.
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You plan to drive north from city A to town B and then continue North to city C. The distance between City A and town B is 39mi and the distance between town B and city C is 99mi.
A. Assuming that you follow a straight driving path, after how many miles of driving will you reach the midpoint between city A and city C?
B. If you drive an average of 46/mi/h how long will it take you to drive from city A to city C?
Here we are given that the distance between city A and B is 39miles and that between city B and C is 99miles . in order to find after how many miles we would reach the midpoint of city A and C , divide the total distance between A and C by 2 as ,
Total distance between A and C =[tex] d_{AB}+d_{BC}[/tex] = 39mi. + 99mi. = 138 miles
Divide this distance by 2 ,
138/2 = 69miles [ answer to Part A ]
_______________
Now the speed is 46miles/hr . In order to find time , use relation,
Speed * time = distance
So that,
time = distance/speed
time = 138/46
time = 3hrs [ answer to Part B ]
and we are done!
If a0=10 and an+1=-5an then find the value of a4
The value of a4 would be equal to -666.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that [tex]a_0=10[/tex] and [tex]a_n+1=-5a_n[/tex]
This is a recursive formula. So we can simply substitute in each value. For instance, a₂
Use the recursive definition repeatedly.
a2 = -5(6) +4 = -26
a3 = -5(-26) +4 = 134
a4 = -5(134) +4 = -666
Therefore, the value of a4 is -666
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mrs. heart asked 100 randomly selected adult americans if they thought that women should be allowed to go into combat situations. here are the results, classified by the gender of the subject. Male= Yes : 18, N0: 32 Famale = Yes: 34, No: 16 What is the probability that a randomly selected subject in the study is Male or answered "No"? A 0.18 B) 0.66 C 0.78 D 0.84
The probability that a randomly selected subject in this is Male or answered 'No' is A: 0.18.
The probability that a randomly selected subject in the study is Male or answered "No" is the sum of the probability that the subject is Male and the probability that the subject answered "No", which is a measure of the overlap between these two events.
To find the probability that a subject is Male, we take the number of Male subjects (50) and divide it by the total number of subjects (100):
P(Male) = 50/100 = 0.5
To find the probability that a subject answered "No", we take the number of subjects who answered "No" (48) and divide it by the total number of subjects (100):
P(No) = 48/100 = 0.48
We can use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the probability that a randomly selected subject is Male or answered "No"
P(Male or No) = P(Male) + P(No) - P(Male and No)
We know that 18 out of 50 Male subjects answered No and 16 out of 50 Female subjects answered no, so the probability that a Male subject answered No is 18/50 = 0.36, and the probability that a Female subject answered No is 16/50 = 0.32
P(Male and No) = P(Male) * P(No|Male) = 0.5 * 0.36 = 0.18
P(Female and No) = P(Female) * P(No|Female) = 0
Hence, the probability that a randomly chosen subject in this is male or answered 'no' is A: 0.18.
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Pls help this is the only one plss
Answer:
1.247 then 1.244 and finally 1.234
Step-by-step explanation:
a local ice cream shop kept track of the number of cans of cold soda it sold each day, and the temperature that day, for 2 months during the summer. the data are displayed in the scatterplot below:
As per the given scatter plot, if the outlier were removed, r would get closer to 1.
The term scatter plot in math is used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another
Here we have given that a local ice cream shop kept track of the number of cans of cold soda it sold each day and the temperature that day, for two months during the summer by using the scatter plot.
Here we have also know that X-axis is temperature measured in degrees Fahrenheit with a range from about 55 to 100 degrees and the value of Y-axis is the number of cans of soda sold with a range from about 165 to 195 cans.
While we take into consideration that a reasonable value of the correlation coefficient r for these data is 1.2.
Where as if the temperature were measured in degrees Celsius (C = 5/9 * (F - 32)), then the value of r would change accordingly.
Thus makes that the correlation coefficient would increase and be closer to 1.
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multiply 101 base two by 11 base two
Answer:
1 1 1 1 to base two
Step-by-step explanation:
1 0 1 base two
× 1 1 base two
+ 1 0 1
1 0 1
=1 1 1 1 base two
Given, y <-x+aandy>x+bIn the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of thefollowing relationship between a and b must be true?A a>bB b>aC |a|> |b|D a = -b
For the given system of inequalities y < -x + a and y > x + b in the xy-plane , the solution represents the relation between a and b is given by :
Option A. a > b.
In the xy -plane given system of inequalities are :
y < -x + a
y > x + b
⇒ x + b < y < -x + a
⇒ x + b < -x + a
⇒ 2x < a - b
Now ( 0, 0 ) is the solution of the given system of inequalities represents :
2(0) < a - b
⇒ a - b > 0
⇒ a > b
Therefore, the relationship between the 'a' and 'b' for the given system of inequalities is given by :
Option A. a > b
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harley was tested 10 times and 9 of those times he choose the correct cup. 1. identify the observational unit and the variable in
The observational unit is Harley and the variable is 0, 1, 2, ..., 10.
When gathering statistical data, information is gathered and statistics are compiled on an observation unit, which is also known as a statistical unit occasionally. An observation is the value of a certain variable at a specific time.
The observational unit in this scenario is Harley and the variable is the number of times Harley chose the correct cup out of 10 trials. The variable can take on the values of 0, 1, 2, ..., 10, where 0 represents the number of incorrect choices and 10 represents the number of correct choices.
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Write a recursive formula for the following arithmetic sequence.
16,13,10,7
a1=
a(n)= blank for n >_ 2
Answer:
a1 = 16
a(n) = a(n-1) -3 for n ≥ 2
Step-by-step explanation:
You want a recursive formula for the arithmetic sequence 16, 13, 10, 7, ....
Arithmetic sequenceThe given sequence has a first term of 16. The common difference is ...
13 -16 = -3
Each successive term is found by adding this difference to the one before. That describes the relation expressed by the recursive formula.
[tex]\begin{cases}a_1=16\\a_n=a_{n-1}-3&\text{for $n\ge2$}\end{cases}[/tex]
For the following exercises, use a calculator to find the length of each side to four decimal places.
In the given right-angled triangle, the sides are 21.3617 and 22.8815.
The given figure is a right-angled triangle. Hence, sides can be determined by using trigonometric function and/or the Pythagorean theorem. It is known that angle A = 69 and side b = 8.2. The side b is an adjacent side to angle A. Using the trigonometric function of tangent
tan Ɵ = opposite side/adjacent side
tan A = a/b
a = b tan A = 8.2 tan 69 ≈ 21.3617
As the two sides a and b are known, the remaining side c can be determined by using Pythagorean theorem,
Hypotenuse^2 = Opposite^2 + Adjacent^2
c^2 = a^2 + b^2
c^2 = (21.3617)^2 + (8.2)^2
c^2 = 523.3635
c =√523.3635
c ≈ 22.8815
Note: The question is incomplete. The complete question probably is: Use a calculator to find the length of each side to four decimal places. (Assume triangle ABC where side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.) side length b = 8.2 and angle A = 69 degrees.
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An aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 84 minutes. The second pipe can fill the tank in 42 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?
It will take 28 minutes for them to fill the tank.
What is work done?Work done is defined as the amount of force needed to move and object a certain distance. In essence, it is a measure of an energy transferred to or from an object which allows it to be moved.
Given that, an aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 84 minutes. The second pipe can fill the tank in 42 minutes by itself.
Work done by first pipe in 1 minute = 1/84
Work done by second pipe in 1 minute = 1/42
The time taken by both the pipes together =
1 / 84 + 1 / 42 = 3 / 84
= 1/28
Therefore, time taken by both the pipe = 28 minutes.
Hence, it will take 28 minutes for them to fill the tank.
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Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to include a percentage sign (96). For all items without specific rounding instructions, round your answers to two decimal places,
show both decimal places (5.06).
Use the graph of a piecewise function with three equations.
25,000
20,000
$21,197-
15,000
10,000
$5,448-5,000
$1,045-
0
20,000 40.000 60,000 80,000
$39,800
$10,450
Taxable Income
a. A taxpayer has a taxable income of $39,800. What is her tax?
b.
A taxpayer will owe $21,197. What is his taxable income?
100,000
$102,800
a. Taxpayer having a taxable income of $39,800 has $5,448 as the income tax.
b. The taxable income of taxpayer owing $21,197 is $102,800.
What is Income Tax?
Income tax is the tax which is levied on all individuals and businesses. The individual income taxes are calculated on the basis of the income received by the individual. Typically, it is categorized as a direct tax because the burden is thought to fall on the people who pay it. Net profits, calculated as the excess of receipts over permitted costs, are subject to corporate income tax.
We are given graph of a piecewise function with three equations which is attached below.
From the graph, it can be observed that the taxpayer who has the taxable income of $39,800 has to pay income tax of $5,448.
Also, a taxpayer owing $21,197 means that he has to pay income tax of $21,197.
His taxable income is $102,800 as shown in the graph below.
Hence, taxpayer having a taxable income of $39,800 has $5,448 as the income tax and the taxable income of taxpayer owing $21,197 is $102,800.
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what is the slope of the line which passes through the origin (-3,5)
Answer:
Step-by-step explanation:
Erick and Mia live the same distance from the park and decide to meet at the park one afternoon. The graphs show
their distances from home over the same 30-minute period as they walked to the park. Each section of each graph
represents 10 minutes.
Distance from Home
Erick
Time
Distance from Home
Mia
Time
Which of the following statements is true?
It took Mia 10 minutes to walk to the park
Mia left home immediately to head to the park
Erick and Mia arrived at the park at different times
It took Frick only 10 minutes to walk to the park
Erick and Mia both live the same distance from the park and decided to meet there one afternoon.
Which of the following statements is true?The graphs show their distances from home over a 30-minute period as they both walked to the park. Each section of each graph represents 10 minutes. From the graphs, it appears that Mia left home immediately to head to the park, while Erick took a few minutes before leaving.This is evidenced by the fact that Mia's graph shows that she was already walking for 10 minutes, while Erick's graph shows that his distance from home had not changed after 10 minutes.Additionally, since Mia's graph is further along than Erick's, this suggests that Mia arrived at the park before Erick. Therefore, it is true that Mia left home immediately to head to the park, and it took her 10 minutes to walk there.However, it took Erick more than 10 minutes to walk to the park, and the two arrived at the park at different times.That it took Mia 10 minutes to walk to the park. Although Erick and Mia left home at the same time, they may have chosen different routes, or one of them may have stopped along the way, so they arrived at the park at different times. It is not stated that it took Erick only 10 minutes to walk to the park.To learn more about The distance refer to:
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29. Candice and Leila arrived at a birthday party at 5:20 p.m. The party lasted for 3 hours. They then took 20 minutes to arrive home. What time did they arrive home?
What is the distributive property of 32+44?
Answer:
66
Step-by-step explanation:
32+44=66
32
+42
____
66
write a function void print int vector(int *ptr, int length) that prints the values in the vector of integers indicated by ptr of length length to the standard output. a vector is a 1-dimensional array. for example, the following c statement declares an integer vector of 10 elements: int avector[10]; each integer should be printed as a decimal number, one entry per line.
The function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output.
The vector is a 1-dimensional array. The formula for this function is:
For i = 0 to length-1
Print ( ptr[i] )
End
The calculation for this function is as follows:
The function starts with a for loop, where the initial value of i is set to 0, and the condition for the for loop is i < length, and the increment value of i is 1. The body of the for loop prints the value of ptr[i], which is the value at the i-th position in the vector. This loop is repeated until the condition i < length is false, at which point the function terminates.
In summary, the function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output. The formula for this function is a for loop, where the initial value of i is set to 0 and the condition for the for loop is i < length. The body of the for loop prints the value of ptr[i], and the loop is repeated until the condition i < length is false.
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Which unit rate corresponds to the proportional relationship shown in the graph?
Drag and drop the answer into the box to match the graph with its unit rate.
A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 12 comma 16 right parenthesis.
1.33 cm/s
Step-by-step explanation:
The line is going from point (0;0) to point (12;16), the proportional relationship between these points refer to the slope of the line, which can be found with this expression:
Replacing all values we have:
Therefore the relation shown in the graph is represented by 1.33 cm/s, which refers to the constant speed developed by the object.
Is this what your looking for if not let me know
Answer:
1.33 cm/s
Step-by-step explanation:
Select the correct answer.
Simplify the following expression.
A.
B.
C.
D.
Cuales son los primeros 10 múltiplos de 18 y 27?
Answer:0, 18, 36, 54, 72, 90, 108, 126, 144, 162
Step-by-step explanation:0 es múltiplo de 18, pues 18 x 0 = 0
18 es múltiplo de 18, pues 18 x 1 = 18
36 es múltiplo de 18, pues 18 x 2 = 36
54 es múltiplo de 18, pues 18 x 3 = 54
72 es múltiplo de 18, pues 18 x 4 = 72
90 es múltiplo de 18, pues 18 x 5 = 90
108 es múltiplo de 18, pues 18 x 6 = 108
126 es múltiplo de 18, pues 18 x 7 = 126
Answer:
Step-by-step explanation:
18: 0, 18, 36, 54, 72, 90, 108, 126, 144, 162
27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270
\item prove that if $f$ is a continuous function defined on an open subset $u$ of $\cc$, then sets of the form $\{z \in u: |f(z)|
The set of all points in an open subset of the complex plane, such that the absolute value of a given continuous function is equal to a given number.
The set of all points in an open subset of the complex plane, such that the absolute value of a given continuous function is equal to a given number, is a set of points that can be found by taking the given continuous function and evaluating it at each point in the open subset of the complex plane. This set of points can be expressed as a set of the form [tex]$\{z \in u: |f(z)|=c\}$[/tex] where u is the open subset of the complex plane and f is the given continuous function. The absolute value of the function must be equal to some number c in order for the point to be included in the set. This set of points is useful for understanding the behavior and properties of the given continuous function on the open subset of the complex plane.
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the manager of a car dealership records the colors of automobiles on a used car lot identify the type of data collected a. quantitative data b.Qualitative c. can be qualitative or quantitative
The records about colors of automobiles on a car lot is a type of qualitative data.
Qualitative data consists of descriptions and characteristics that are difficult to quantify but easy to perceive in the human senses, such as smell, food, gender, country, and color. Observations, individual interviews, focus groups, and other similar procedures are used to get this information. Categorical data is another name for qualitative data in statistics; it refers to information that may be sorted into groups based on the characteristics of a given entity or event. Qualitative data are also known as categorical data since they may be sorted into categories.
When trying to determine the exact frequency of certain features or attributes, qualitative data is a very useful tool. It gives the statistician or the researcher the ability to generate parameters that can be used to examine larger data sets.
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peter's international barbershop is a popular haircutting and styling saloon near the campus of the brooklyn college. one barber is available to work full time and spend an average of 4 minutes on each customer. customers arrive all day long at an average rate of 5 minutes arrivals tend to follow the poisson distribution, and service times are exponentially distributed. explain your results. [5 points]
If we assume that the average rate of arrivals is 5 minutes, then this means that the Poisson distribution will have a mean of 5 customers/minutesThis means that the probability that a customer arrives in the next minute is 0.2 (1/5).
The exponential distribution will have a mean of 4 minutes, meaning that the probability that the customer is served in the next minute is 0.25 (1/4).
Therefore, the expected number of customers that the barber can serve in an hour is 15 (5*4). The expected number of customers served in a given minute is 0.2 (1/5) * 0.25 (1/4) = 0.05. This means that the barber can expect to serve an average of 3 customers per hour.
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Consider a function f defined as follows: f(x)=(x-3)^2, x belongs to [1,2]. Is f invertible in the domain [1,2]? If yes, find the inverse of the function.
(Need a detailed explanation showing the function is invertible, then determining the inverse.)
The function f(x) = (x - 3)² is invertible on the interval [1,2], as each output is related only with a single input.
The inverse of the function is given as follows:
[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]
How to obtain the inverse function?The function for this problem is defined as follows:
f(x) = (x - 3)²
The x-coordinate of the vertex of the quadratic function is given as follows:
x = 3.
Hence the function is invertible on the domain [1,2], which is entirely on one side of the vertex, and thus each output is related only with a single input.
The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:
x = (y - 3)²
[tex]y - 3 = -\sqrt{x}[/tex]
[tex]y = -\sqrt{x} - 3[/tex]
[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]
The negative symbol is because the function is on the left side of the vertex.
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solve the equation: x2+7x=0
Answer: X=
Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get
and
as your answers, then enter 4,-2/3 in the box.
The solution to the given equation x² + 7x = 0 is x = 0, -7.
What is a quadratic equation?The quadratic equation is defined as a function containing the highest power of a variable is two.
The quadratic equation is given in the question, as follows:
x² + 7x = 0
We have to determine the solution to the given equation.
As per the question, we have
x² + 7x = 0
x(x + 7) = 0
Equating factors to zero, we get
x = 0 and (x + 7) = 0
x = 0 and x = -7
Thus, the solution to the given equation is x = 0, -7.
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10) A boat travels 30 km up a river in the same time it takes to travel 50 km down the same river. If the current of water is 5km/h. What is the speed of the boat in still water? Be sure to show your work to earn full credit. Here's a chart to get you started: Travel Rate Time Distance
As a result, when a boat goes 30 km up a river in the same amount of time, its speed in still water is 20 km/h.
what is equation ?The numeral is said to be in this simplest form when divided into its smallest equivalent fraction. How to do to find the most basic form. Find common factors in the denominator and numerators. Verify a fractional integer to verify if it passes as a prime number. A statement having two collinear and an equally sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The normal form of a linear function is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorised as identities or conditional equations. An identity holds true regardless of the value given to the variables.
given
Let the boat's speed in calm water be x km/h.
Boat speed downstream is equal to x plus 5.
Upstream boat speed is equal to x - 5
Distance x time speed
Time is therefore determined by speed and distance.
Boat travel time is equal to 30/km upstream (x – 5)
50/(x + 5) is the time it takes a boat to travel 50 kilometres downstream.
Since the boat takes the same amount of time in both scenarios, 30 (x + 5) = 50 (x -5), 30 x +150 = 50 (x -250), 20 (x = 400), and 20 (x = 20).
As a result, when a boat goes 30 km up a river in the same amount of time, its speed in still water is 20 km/h.
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a car dealer is deciding what kinds of vehicles he should order from the factory. he looks at his sales report for the preceding period. construct a pareto chart to help him decide. choose the vertical scale so that the relative frequencies are represented.
The vertical scales for each type of vehicle are:
Economy, 0.2Sports, 0.5Family, 0.35Luxury, 0.1Truck, 0.3The rationale is to choose a vertical scale that represents the relative frequencies, or the proportion of each type of vehicle sold compared to the total number of vehicles sold. The calculation for each type of vehicle is as follows:
Economy: 30 / 150 = 0.2 Sports: 7.5 / 150 = 0.05Family: 52.5 / 150 = 0.35 Luxury: 15 / 150 = 0.1 Truck: 45 / 150 = 0.3Here, the total number of vehicles sold (150) is calculated by adding up the sales for each type of vehicle. The relative frequency for each type of vehicle is then calculated by dividing the sales for that type of vehicle by the total number of vehicles sold.
This question should be provided as:
A car dealer is deciding what kind of vehicles he should order from the factory. he looks at his sales report for the preceding period. choose the vertical scale so that the relative frequencies are represented:
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. Max needs 104 cups of flour to make a batch
of pizza dough for the pizzeria. He only has
4 cups of flour. How much more flour does
he need to make the dough? (STEP BY STEP. FOR THE LAST TIME.)
To make the dough, he'll need 5 3/4 cups of floor.
What is fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a portion or part of a whole. It symbolizes the equal parts of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator.
Here,
10 1/4 cups of flour needed to make a batch=41/4 cups
4 1/2 cups of floor is there=9/2 cups
flour does he need to make the dough,
=41/4-9/2
=(41-18)/4
=23/4
=5 3/4 cups
He needs 5 3/4 cups of floor to make the dough.
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Find domain and range of the relation: (-2,7), (-2,6), (-2,5), (-2,4).
Then determine whether the relation of a function (yes or no).
The domain and range of the relation are { -2 } and { 4, 5, 6, 7 } respectively. The relation is not a function.
Is the relation a function? What are the domain and range?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the relation in the question;
(-2,7), (-2,6), (-2,5), (-2,4)
For a relation to be a function, every x-value must have only one y-value mapped to it.
-2 appeared twice and its corresponding y-values are different.
Hence, the relation is Not a Function.
The Domains are the x-values and the Range are the y-values,
Domain: { -2 }
Range: { 4, 5, 6, 7 }
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Drag the files to the correct boxes to complete the pairs make each system of linear equations with the correct number of solutions 
The number of solutions for given three system of linear equations.
We can simply solve this numerical problem by using the following process.
3x - y = 4 ==> a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2
What is meant by numerical?
The phrase "numerical" refers to something that involves numbers.Numerical expression is made up of the two words numerical, which refers to numbers, and expression, which refers to a statement. Consequently, it is a statement that uses numbers.A numerical solution entails speculating about the answer and determining if the issue is sufficiently resolved to end.This formula has numerous complicated terms, making it difficult to recall. Additionally, finding a solution takes time. There are instances when a system has access to a lot of data, and the data can also be analyzed to find a solution. But because there is so much data, finding a solution to these issues takes time.Based on the formula is:
Let the system of equations be a₁x + b₁y = c₁ and a₂x + b₂y = c₂ then
Condition for One solution: a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
Condition for No Solution: a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Condition for infinitely many solutions: a₁/a₂ = b₁/b₂ = c₁/c₂
Now in the given question:
a.) 3x - y = 4
6x - 2y = 8
⇒ a₁/a₂=3/6 = 1/2 ; b₁/b₂ = -1/-2 = 1/2 ; c₁/c₂ = 4/8 = 1/2
⇒ a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2
The given system of equations is coincident lines, hence has infinitely many solutions.
b.) -3x + y = 7
2x - 4y = -8
⇒ a₁/a₂= -3/2 ; b₁/b₂ = 1/-4 ; c₁/c₂ = 7/-8
⇒ a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
The given system of equations is intersecting lines, hence having a single solution.
c.) y = -4x - 5
y = -4x +1
⇒ a₁/a₂= -4/-4 = 1 ; b₁/b₂ = 1/1 = 1 ; c₁/c₂ = -5/1 = -5
⇒ a₁/a₂ = b₁/b₂ ≠ c₁/c₂
The given system of equations is parallel lines, hence having no solution.
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